Dada la función f(x)=1+6Sen(2x+π/3) . Halle: Período, amplitud y desfase (1.5 puntos) Dominio y rango de la función (1.5 puntos) Grafique la función trigonométrica (2 puntos)

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06-07-2021
Mathematics

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Dada la función f(x)=1+6Sen(2x+π/3) . Halle: Período, amplitud y desfase (1.5 puntos) Dominio y rango de la función (1.5 puntos) Grafique la función trigonométrica (2 puntos)

Sagot :

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jaimitoM jaimitoM · Answer 1 · 2021-07-07T00:27:55-04:00

Dada una ecuación de la forma

y = A sin(B(x + C)) + D

Tenemos que:

la amplitud es A
el periodo es 2π/B
el desfase es C (a la izquierda es positivo)
el desplazamiento vertical es D

Sabemos que:

f(x)=1+6Sen(2x+π/3)

Y podemos reescribirla como:

f(x)=6Sen(2(x+π/6))+1

Siendo:

A = 6 → Amplitud
T = 2π/B = 2π/2 = π → Período
C = π/6 → Desfase
El dominio de un a función trigonométrica es todo el conjunto de los números reales (x ∈ R ).

La imagen de una función trigonométrica de esta forma es:

y ∈ [-A+D,A+D]

y ∈ [-6+1, 6+1]

y ∈ [-5,7]

La gráfica se adjunta.

Dada la función f(x)=1+6Sen(2x+π/3) . Halle: Período, amplitud y desfase (1.5 puntos) Dominio y rango de la función (1.5 puntos) Grafique la función trigonométrica (2 puntos)

Sagot :

y = A sin(B(x + C)) + D

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